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Difficulty: HardComparison of Market Structures: Economic Efficiency and Consumer Welfare

Suppose a market demand function is given by P=100−2QP = 100 - 2Q, where PP is the price in dollars and QQ is the output quantity. The market operates at a constant marginal cost of MC=$20MC = \$20 with no fixed costs. If this market transitions from perfect competition to a monopoly, by how much is consumer welfare (consumer surplus) reduced?

  1. A
    $400
  2. B
    $800
  3. $1,200Answer
  4. D
    $1,600

Answer

Consumer welfare (consumer surplus) is reduced by $1,200.
Under perfect competition, allocative efficiency is achieved where price equals marginal cost (P=MC=20P = MC = 20), yielding an output of 40 units and a consumer surplus of 12×(100−20)×40=$1,600\frac{1}{2} \times (100 - 20) \times 40 = \$1,600. When monopolized, profit maximization requires setting marginal revenue equal to marginal cost (MR=MCMR = MC), where MR=100−4QMR = 100 - 4Q. Solving gives Q=20Q = 20 units and a higher price of P=$60P = \$60. The new consumer surplus under monopoly is 12×(100−60)×20=$400\frac{1}{2} \times (100 - 60) \times 20 = \$400. The total reduction in consumer welfare is $1,600−$400=$1,200\$1,600 - \$400 = \$1,200.

Step-by-Step Solution

1
Calculate price, quantity, and consumer surplus under perfect competition.
Competitive price Pc=$20P_c = \$20, quantity Qc=40Q_c = 40 units, and consumer surplus CSc=$1,600CS_c = \$1,600.
In perfect competition, price equals marginal cost (P=MCP = MC). Setting 100−2Q=20100 - 2Q = 20 yields Qc=40Q_c = 40. At Q=0Q = 0, the maximum willingness to pay is 100.Consumersurplusistheareaofthetriangle:100. Consumer surplus is the area of the triangle: \frac{1}{2} \times (100 - 20) \times 40 = 1,600$.
2
Derive the marginal revenue equation and calculate price and quantity under monopoly.
Monopoly quantity Qm=20Q_m = 20 units and monopoly price Pm=$60P_m = \$60.
Total revenue is TR=P×Q=100Q−2Q2TR = P \times Q = 100Q - 2Q^2, so MR=100−4QMR = 100 - 4Q. Setting MR=MCMR = MC gives 100−4Q=20  ⟹  Qm=20100 - 4Q = 20 \implies Q_m = 20. Substituting into the demand function yields Pm=100−2(20)=60P_m = 100 - 2(20) = 60.
3
Calculate consumer surplus under monopoly.
Monopoly consumer surplus CSm=$400CS_m = \$400.
Consumer surplus under monopoly is the area between the demand curve and monopoly price: 12×(100−60)×20=400\frac{1}{2} \times (100 - 60) \times 20 = 400.
4
Calculate the reduction in consumer welfare (consumer surplus).
Reduction in consumer surplus ΔCS=1,600−400=1,200\Delta CS = 1,600 - 400 = 1,200.
Subtract monopoly consumer surplus from competitive consumer surplus (CSc−CSm=1,600−400=1,200CS_c - CS_m = 1,600 - 400 = 1,200).

Key Concept

Monopoly Welfare Loss and Consumer Surplus Comparison
Estimated Time:2m 30s
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Topics

Comparison of Market Structures: Economic Efficiency and Consumer Welfare

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